Methods of designing high x-ray lucency lattice structures

ABSTRACT

The biocompatible lattice structures disclosed herein with an increased or optimized lucency are prepared according to multiple methods of design disclosed herein. The methods allow for the design of a metallic material with sufficient strength for use in an implant and that remains radiolucent for x-ray imaging.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 62/458,714 filed Feb. 14, 2017, U.S. Provisional PatentApplication No. 62/480,383 filed Apr. 1, 2017, U.S. Provisional PatentApplication No. 62/480,385 filed Apr. 1, 2017, and U.S. ProvisionalPatent Application No. 62/619,260 filed Jan. 19, 2018, which are herebyincorporated by reference in their entirety.

FIELD OF THE INVENTION

The present invention relates to biocompatible lattice structures and,in particular, to lattice structures with increased lucency in a desireddirection with respect to x-ray imaging and to markers with a variableradiolucency or radiopacity.

BACKGROUND OF THE INVENTION

Medical implants can be constructed using a wide range of materials,including metallic materials, Polyether ether ketone (hereinafter“PEEK”), ceramic materials and various other materials or compositesthereof. There are competing priorities when selecting a material for animplant in order for the implant to pass regulatory testing. Somepriorities when designing an implant could include strength, stiffness,fatigue resistance, radiolucency, and bioactivity. Therefore, whendesigning an implant to meet regulatory standards, oftentimes, somecompromises have to be made to meet all testing requirements.

BRIEF SUMMARY OF THE INVENTION

The biocompatible lattice structures disclosed herein, in someembodiments, have an increased lucency. Also disclosed herein is amethod of designing lattice structure with an increased lucency. Someembodiments also include markers with a varied radiolucency based on theviewing angle.

The lattice structures disclosed herein can have increased lucency overother structures comprising similar materials, porosities, densitiesand/or volumetric densities. While the embodiments expressed herein aredirected towards medical implants, the structures disclosed could alsobe beneficial when used in medical devices outside of the body thatrequire a level of lucency or in devices outside of the medical field.

When implants comprise lattice structures or scaffolds for tissuegrowth, it is desirable to be able to monitor the healing process withinthe implant. In many cases, it is beneficial to be able to monitor thelevel of bone ingrowth at certain time intervals after implantation.Generally, imaging of the surgical site is completed using x-rayimaging, however, other types of imaging may also be used.

Many biocompatible structures, including lattice or porous structures,comprise a material generally considered to have radiopaque properties.It was discovered that materials that are generally considered to beradiopaque often only become fully radiopaque when a certain bulkthickness is reached. In this case, bulk thickness means the actualthickness of a structure in a certain direction when any voids areremoved. For instance, a structure with a uniform 50% volumetric densityand a thickness of two inches would have a bulk thickness of one inch inthat direction and a lattice with a 25% volumetric density and athickness of two inches would have a bulk thickness of a half inch inthat direction.

The elastic modulus of lattice structures may be modified by changingthe volumetric density of the structure so that increasing thevolumetric density generally increases the bulk elastic modulus and viceversa. Depending on the particular elastic modulus needed in anapplication, the need for radiolucency can be at odds with the need foran increased elastic modulus. Therefore, the lattice structures andmethods of design disclosed herein are particularly useful in implantswhere there is a need for a lattice structure with increased lucency atall volumetric density levels.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 is an isometric view of a single modified rhombic dodecahedronunit cell containing a full modified rhombic dodecahedron structurealong with radial struts that comprise portions of adjacent unit cells.

FIG. 2 is a side view of a single modified rhombic dodecahedron unitcell showing the configuration of interconnections when viewed from alateral direction.

FIG. 3 is a side view of a single modified rhombic dodecahedron unitcell where the central void is being measured using the longestdimension method.

FIG. 4 is a side view of a single modified rhombic dodecahedron unitcell where an interconnection is being measured using the longestdimension method.

FIG. 5 is a side view of the central void of a modified rhombicdodecahedron unit cell being measured with the largest sphere method.

FIG. 6 is a view from a direction normal to the planar direction of aninterconnection being measured with the largest sphere method.

FIG. 7 is an isometric view of a single radial dodeca-rhombus unit cell.

FIG. 8 is a side view of a single radial dodeca-rhombus unit cell.

FIG. 9 is an isometric view of an example of a single node and singlestrut combination that could be used in a radial dodeca-rhombus unitcell.

FIG. 10 is a side view of an example of a single node and single strutcombination that could be used in a radial dodeca-rhombus unit cell.

FIG. 11 is a side view of a single node and single strut combinationconfigured for use in a lattice with an elastic modulus of approximately3 GPa, viewed from the corner of the volume defining the bounds of thecombination.

FIG. 12 is a side view of a single node and single strut combinationconfigured for use in a lattice with an elastic modulus of approximately4 GPa, viewed from the corner of the volume defining the bounds of thecombination.

FIG. 13 is a side view of a single node and single strut combinationconfigured for use in a lattice with an elastic modulus of approximately10 GPa, viewed from the corner of the volume defining the bounds of thecombination.

FIG. 14 is a side view of a single node and two adjacent struts viewedfrom the corner of the volume defining the bounds of the combination andthe lateral separation angle.

FIG. 15 is an isometric view of a sub-unit cell comprised of a singlenode and four struts.

FIG. 16 is an isometric view of two sub-unit cells in a stackedformation where the upper sub-unit cell is inverted and fixed to the topof the lower sub-unit cell.

FIG. 17 is an isometric view of eight sub-unit cells stacked together toform a single unit cell.

FIG. 18 is a perspective view of an example of the invention using acubic unit cell and rotated 23 degrees about the z axis and 33.67degrees about the x axis from a normal face.

FIG. 19 is a perspective view of an example of the invention using acubic unit cell and rotated 22 degrees about the z axis and 30 degreesabout the x axis from a normal face.

FIG. 20 is a perspective view of an example of the invention using acubic unit cell and rotated 45 degrees about the z and x axes from anormal face.

FIG. 21 is a perspective view of an example of the invention using acubic unit cell and rotated 45 degrees along x axis from a normal face.

FIG. 22 is a perspective view of an example of the invention using acubic unit cell with no rotation from a normal face.

FIG. 23 is an isometric view of a first exemplary embodiment of thevariable lucent markers (hereinafter “variable markers”) comprised offilled unit cells and shown in a misaligned direction.

FIG. 24 is a side view of a first exemplary embodiment of the variablemarkers comprised of filled unit cells and shown in a misaligneddirection.

FIG. 25 is an isometric view of a second exemplary embodiment of thevariable markers comprised of partially filled unit cells and shown in amisaligned direction.

FIG. 26 is a side view of a second exemplary embodiment of the variablemarkers comprised of partially filled unit cells and shown in an aligneddirection.

FIG. 27 is an alternative side view of a second exemplary embodiment ofthe variable markers comprised of partially filled unit cells and shownin a second aligned direction.

FIG. 28 is an isometric view of a third exemplary embodiment of thevariable markers comprised of enlarged nodes and shown in a misaligneddirection.

FIG. 29 is an offset side view of a third exemplary embodiment of thevariable markers comprised of enlarged nodes and shown in a misaligneddirection that is approaching an aligned direction.

FIG. 30 is a top view of a third exemplary embodiment of the variablemarkers comprised of enlarged nodes and shown in an aligned direction.

FIG. 31 is a side view of a third exemplary embodiment of the variablemarkers comprised of enlarged nodes and shown in an aligned direction.

FIG. 32 is an isometric view of a fourth exemplary embodiment of thevariable markers also comprised of enlarged nodes and shown in amisaligned direction.

FIG. 33 is an isometric view of a fifth exemplary embodiment of thevariable markers comprised of enlarged struts and shown in a misaligneddirection.

FIG. 34 is a side view of a fifth exemplary embodiment of the variablemarkers comprised of enlarged struts and shown in an aligned direction.

FIG. 35 is a side view of an exemplary interbody fusion implantincorporating variable markers shown in an aligned direction.

FIG. 36 is a perspective view of an exemplary interbody fusion implantincorporating variable markers shown in a misaligned direction.

FIG. 37 is an example of an interbody fusion implant, designed using thehigh x-ray lucency lattice and methods of designing a high x-ray lucencylattice disclosed herein, and imaged on an x-ray machine in the anteriorto posterior direction.

FIG. 38 is an example of an interbody fusion implant, designed using thehigh x-ray lucency lattice and methods of designing a high x-ray lucencylattice disclosed herein, and imaged on an x-ray machine in a lateraldirection.

DETAILED DESCRIPTION OF THE INVENTION

In many situations, it is desirable to use an implant that is capable ofbone attachment or osteointegration over time. It is also desirable inmany situations to use an implant that is capable of attachment orintegration with living tissue. Examples of implants where attachment tobone or osteointegration is beneficial include, but are not limited to,cervical, lumbar, and thoracic interbody fusion implants, vertebral bodyreplacements, osteotomy wedges, dental implants, bone stems, acetabularcups, cranio-facial plating, bone replacement and fracture plating. Inmany applications, it is also desirable to stress new bone growth toincrease its strength. According to Wolff's law, bone will adapt tostresses placed on it so that bone under stress will grow stronger andbone that isn't stressed will become weaker.

In some aspects, the systems and methods described herein can bedirected toward implants that are configured for osteointegration andstimulating adequately stressed new bone growth. Many of the exemplaryimplants of the present invention are particularly useful for use insituations where it is desirable to have strong bone attachment and/orbone growth throughout the body of an implant. Whether bone growth isdesired only for attachment or throughout an implant, the presentinvention incorporates a unique lattice structure that can providemechanical spacing, a scaffold to support new bone growth and a modulusof elasticity that allows new bone growth to be loaded withphysiological forces. As a result, the present invention providesimplants that grow stronger and healthier bone for more secureattachment and/or for a stronger bone after the implant osteointegrates.

The exemplary embodiments of the invention presented can be comprised,in whole or in part, of a lattice. A lattice, as used herein, refers toa three-dimensional material with one or more interconnected openingsthat allow a fluid to communicate from one location to another locationthrough an opening. A three-dimensional material refers to a materialthat fills a three-dimensional space (i.e. has height, width andlength). Lattices can be constructed by many means, including repeatingvarious geometric shapes or repeating random shapes to accomplish amaterial with interconnected openings. An opening in a lattice is anyarea within the bounds of the three-dimensional material that is devoidof that material. Therefore, within the three-dimensional boundaries ofa lattice, there is a volume of material and a volume that is devoid ofthat material.

The material that provides the structure of the lattice is referred toas the primary material. The structure of a lattice does not need toprovide structural support for any purpose, but rather refers to theconfiguration of the openings and interconnections that comprise thelattice. An opening in a lattice may be empty, filled with a gaseousfluid, filled with a liquid fluid, filled with a solid or partiallyfilled with a fluid and/or solid. Interconnections, with respect toopenings, refer to areas devoid of the primary material and that link atleast two locations together. Interconnections may be configured toallow a fluid to pass from one location to another location.

A lattice can be defined by its volumetric density, meaning the ratiobetween the volume of the primary material and the volume of voidspresented as a percentage for a given three-dimensional material. Thevolume of voids is the difference between the volume of the bounds ofthe three-dimensional material and the volume of the primary material.The volume of voids can comprise of the volume of the openings, thevolume of the interconnections and/or the volume of another materialpresent. For example, a lattice with a 30% volumetric density would becomprised of 30% primary material by volume and 70% voids by volume overa certain volume. A lattice with a 90% volumetric density would becomprised of 90% primary material by volume and 10% voids by volume overa certain volume. In three-dimensional materials with a volumetricdensity of less than 50%, the volume of the primary material is lessthan the volume of voids. While the volumetric density refers to thevolume of voids, the voids do not need to remain void and can be filled,in whole or in part, with a fluid or solid prior to, during or afterimplantation.

Lattices comprised of repeating geometric patterns can be describedusing the characteristics of a repeating unit cell. A unit cell in arepeating geometric lattice is a three-dimensional shape capable ofbeing repeated to form a lattice. A repeating unit cell can refer tomultiple identical unit cells that are repeated over a lattice structureor a pattern through all or a portion of a lattice structure. Each unitcell is comprised of a certain volume of primary material and a certainvoid volume, or in other words, a spot volumetric density. The spotvolumetric density may cover as few as a partial unit cell or aplurality of unit cells. In many situations, the spot volumetric densitywill be consistent with the material's volumetric density, but there aresituations where it could be desirable to locally increase or decreasethe spot volumetric density.

Unit cells can be constructed in numerous volumetric shapes containingvarious types of structures. Unit cells can be bound by a defined volumeof space to constrict the size of the lattice structure or other type ofstructure within the unit cell. In some embodiments, unit cells can bebound by volumetric shapes, including but not limited to, a cubicvolume, a cuboid volume, a hexahedron volume or an amorphous volume. Theunit cell volume of space can be defined based on a number of faces thatmeet at corners. In examples where the unit cell volume is a cubic,cuboid or hexahedron volume, the unit cell volume can have six faces andeight corners, where the corners are defined by the location where threefaces meet. Unit cells may be interconnected in some or all areas, notinterconnected in some or all areas, of a uniform size in some or allareas or of a nonuniform size in some or all areas. In some embodimentsdisclosed herein that use a repeating geometric pattern, the unit cellscan be defined by a number of struts defining the edges of the unit celland joined at nodes about the unit cell. Unit cells so defined can sharecertain struts among more than one unit cell, so that two adjacent unitcells may share a common planar wall defined by struts common to bothcells. In some embodiments disclosed herein that use a repeatinggeometric pattern, the unit cells can be defined by a node and a numberof struts extending radially from that node.

While the present application uses volumetric density to describeexemplary embodiments, it is also possible to describe them using othermetrics, including but not limited to cell size, strut size orstiffness. Cell size may be defined using multiple methods, includingbut not limited to cell diameter, cell width, cell height and cellvolume. Strut size may be defined using multiple methods, including butnot limited to strut length and strut diameter.

Repeating geometric patterns are beneficial for use in latticestructures contained in implants because they can provide predictablecharacteristics. Many repeating geometric shapes may be used as the unitcell of a lattice, including but are not limited to, rhombicdodecahedron, diamond, dodecahedron, square, pentagonal, hexagonal,octagonal, sctet struts, trunic octa, diagonal struts, other knowngeometric structures, and rounded, reinforced, weakened, or simplifiedversions of each geometry.

Lattices may also be included in implants as a structural component or anonstructural component. Lattices used in structural applications may bereferred to herein as structural lattices, load-bearing lattices orstressed lattices. In some instances, structural lattices, load-bearinglattices or stressed lattices may be simply referred to as a lattice.Repeating geometric shaped unit cells, particularly the rhombicdodecahedron, are well suited, in theory, for use in structural latticesbecause of their strength to weight ratio. To increase the actualstrength and fatigue resistance of a rhombic dodecahedron lattice, thepresent invention, in some embodiments, includes a modified strutcomprised of triangular segments, rather than using a strut with arectangular or circular cross section. Some embodiments herein alsomodify the angles defining the rhombic faces of a rhombic dodecahedronto change the lattice's elastic modulus and fatigue resistance. The useof triangular segments provides a lattice with highly predictableprinted properties that approach the theoretical strength values for arhombic dodecahedron lattice.

In structural lattice applications, the strength and elastic modulus ofthe lattice can be approximated by the volumetric density. When thevolumetric density increases, the strength and the elastic modulusincreases. Compared to other porous structures, the lattice of thepresent invention has a higher strength and elastic modulus for a givenvolumetric density because of its ability to use the high strength toweight benefits of a rhombic dodecahedron, modified rhombic dodecahedronor radial dodeca-rhombus unit cell.

When configured to provide support for bone or tissue growth, a latticemay be referred to as a scaffold. Lattices can be configured to supportbone or tissue growth by controlling the size of the openings andinterconnections disposed within the three-dimensional material. Ascaffold, if used on the surface of an implant, may provide anosteointegration surface that allows adjacent bone to attach to theimplant. A scaffold may also be configured to provide a path that allowsbone to grow further than a mere surface attachment. Scaffolds intendedfor surface attachment are referred to herein as surface scaffolds. Asurface scaffold may be one or more unit cells deep, but does not extendthroughout the volume of an implant. Scaffolds intended to supportin-growth beyond mere surface attachment are referred to herein as bulkscaffolds. Scaffolds may also be included in implants as a structuralcomponent or a nonstructural component. Scaffolds used in structuralapplications may be referred to herein as structural scaffolds,load-bearing scaffolds or stressed scaffolds. In some instances,structural scaffolds, load-bearing scaffolds or stressed scaffolds maybe simply referred to as a scaffold. In some instances, the use of theterm scaffold may refer to a material configured to provide support forbone or tissue growth, where the material is not a lattice.

The scaffolds described herein can be used to promote the attachment orin-growth of various types of tissue found in living beings. As notedearlier, some embodiments of the scaffold are configured to promote boneattachment and in-growth. The scaffolds can also be configured topromote attachment of in-growth of other areas of tissue, such asfibrous tissue. In some embodiments, the scaffold can be configured topromote the attachment or in-growth of multiple types of tissue. Someembodiments of the scaffolds are configured to be implanted near orabutting living tissue. Near living tissue includes situations whereother layers, materials or coatings are located between a scaffold andany living tissue.

In some embodiments, the present invention uses bulk scaffolds withopenings and interconnections that are larger than those known in theart. Osteons can range in diameter from about 100 μm and it is theorizedthat a bundle of osteons would provide the strongest form of new bonegrowth. Bone is considered fully solid when it has a diameter of greaterthan 3 mm so it is theorized that a bundle of osteons with a diameterequaling approximately half of that value would provide significantstrength when grown within a scaffold. It is also theorized that osteonsmay grow in irregular shapes so that the cross-sectional area of anosteon could predict its strength. A cylindrical osteon growth with a 3mm diameter has a cross-sectional area of approximately 7 square mm anda cylindrical osteon with a 1.5 mm diameter has a cross-sectional areaof 1.8 square mm. It is theorized that an osteon of an irregular shapewith a cross-sectional area of at least 1.8 square millimeters couldprovide a significant strength advantage when grown in a scaffold.

Most skilled in the art would indicate that pores or openings with adiameter or width between 300 μm to 900 μm, with a pore side of 600 μmbeing ideal, provide the best scaffold for bone growth. Instead, someembodiments of the present invention include openings andinterconnections with a diameter or width on the order of 1.0 to 15.0times the known range, with the known range being 300 μm to 900 μm,resulting in openings from 0.07 mm² up to 145 mm² cross sectional areafor bone growth. In some examples, pores or openings with a diameter orwidth between and including 100 μm to 300 μm could be beneficial. Someexamples include openings and interconnections with a diameter on theorder of 1.0 to 5.0 times the known range. It has been at leasttheorized that the use of much larger openings and interconnections thanthose known in the art will allow full osteons and solid bone tissue toform throughout the bulk scaffold, allowing the vascularization of new,loadable bone growth. In some examples, these pores may be 3 mm indiameter or approximately 7 mm² in cross sectional area. In otherexamples, the pores are approximately 1.5 mm in diameter orapproximately 1.75 mm² in cross sectional area. The use of only thesmaller diameter openings and interconnections known in the art aretheorized to limit the penetration of new bone growth into a bulkscaffold because the smaller diameter openings restrict the ability ofvascularization throughout the bulk scaffold.

A related structure to a lattice is a closed cell material. A closedcell material is similar to a lattice, in that it has openings containedwithin the bounds of a three-dimensional material, however, closed cellmaterials generally lack interconnections between locations throughopenings or other pores. A closed cell structure may be accomplishedusing multiple methods, including the filling of certain cells orthrough the use of solid walls between the struts of unit cells. Aclosed cell structure can also be referred to as a cellular structure.It is possible to have a material that is a lattice in one portion and aclosed cell material in another. It is also possible to have a closedcell material that is a lattice with respect to only certaininterconnections between openings or vice versa. While the focus of thepresent disclosure is on lattices, the structures and methods disclosedherein can be easily adapted for use on closed cell structures withinthe inventive concept.

The lattice used in the present invention can be produced from a rangeof materials and processes. When used as a scaffold for bone growth, itis desirable for the lattice to be made of a biocompatible material thatallows for bone attachment, either to the material directly or throughthe application of a bioactive surface treatment. In one example, thescaffold is comprised of an implantable metal. Implantable metalsinclude, but are not limited to, zirconium, stainless steel (316 &316L), tantalum, nitinol, cobalt chromium alloys, titanium and tungsten,and alloys thereof. Scaffolds comprised of an implantable metal may beproduced using an additive metal fabrication or 3D printing process.Appropriate production processes include, but are not limited to, directmetal laser sintering, selective laser sintering, selective lasermelting, electron beam melting, laminated object manufacturing anddirected energy deposition.

In another example, the lattice of the present invention is comprised ofan implantable metal with a bioactive coating. Bioactive coatingsinclude, but are not limited to, coatings to accelerate bone growth,anti-thrombogenic coatings, anti-microbial coatings, hydrophobic orhydrophilic coatings, and hemophobic, superhemophobic, or hemophiliccoatings. Coatings that accelerate bone growth include, but are notlimited to, calcium phosphate, hydroxyapatite (“HA”), silicate glass,stem cell derivatives, bone morphogenic proteins, titanium plasma spray,titanium beads and titanium mesh. Anti-thrombogenic coatings include,but are not limited to, low molecular weight fluoro-oligomers.Anti-microbial coatings include, but are not limited to, silver,organosilane compounds, iodine and silicon-nitride. Superhemophobiccoatings include fluorinated nanotubes.

In another example, the lattice is made from a titanium alloy with anoptional bioactive coating. In particular, Ti6Al4V ELI wrought (AmericanSociety for Testing and Materials (“ASTM”) F136) is a particularlywell-suited titanium alloy for scaffolds. While Ti6Al4V ELI wrought isthe industry standard titanium alloy used for medical purposes, othertitanium alloys, including but not limited to, unalloyed titanium (ASTMF67), Ti6Al4V standard grade (ASTM F1472), Ti6Al7Nb wrought (ASTM 1295),Ti5Al2.5Fe wrought (British Standards Association/International StandardOrganization Part 10), CP and Ti6Al4V standard grade powders (ASTMF1580), Ti13Nb13Zr wrought (ASTM F1713), the lower modulusTi-24Nb-4Zr-8Sn and Ti12Mo6Zr2Fe wrought (ASTM F1813) can be appropriatefor various embodiments of the present invention.

Titanium alloys are an appropriate material for scaffolds because theyare biocompatible and allow for bone attachment. Various surfacetreatments can be done to titanium alloys to increase or decrease thelevel of bone attachment. Bone will attach to even polished titanium,but titanium with a surface texture allows for greater bone attachment.Methods of increasing bone attachment to titanium may be producedthrough a forging or milling process, sandblasting, acid etching, andthe use of a bioactive coating. Titanium parts produced with an additivemetal fabrication or 3D printing process, such as direct metal lasersintering, can be treated with an acid bath to reduce surface stressrisers, normalize surface topography, and improve surface oxide layer,while maintaining surface roughness and porosity to promote boneattachment.

Additionally, Titanium or other alloys may be treated with heparin,heparin sulfate (HS), glycosaminoglycans (GAG), chondroitin-4-sulphate(C4S), chondroitin-6-sulphate (C6S), hyaluronan (HY), and otherproteoglycans with or without an aqueous calcium solution. Suchtreatment may occur while the material is in its pre-manufacturing form(often powder) or subsequent to manufacture of the structure.

While a range of structures, materials, surface treatments and coatingshave been described, it is believed that a lattice using a repeatingmodified rhombic dodecahedron (hereinafter “MRDD”) unit cell can presenta preferable combination of stiffness, strength, fatigue resistance, andconditions for bone ingrowth. In some embodiments, the repeating MRDDlattice is comprised of titanium or a titanium alloy. A generic rhombicdodecahedron (hereinafter “RDD”), by definition, has twelve sides in theshape of rhombuses. When repeated in a lattice, an RDD unit cell iscomprised of twenty four struts that meet at fourteen vertices. Thetwenty four struts define the twelve planar faces of the structure. Anopening or interconnection is disposed at the center of each planarface, allowing communication from inside the unit cell to outside theunit cell.

An example of the MRDD unit cell 10 used in the present invention isshown in FIGS. 1-5. FIG. 1 illustrates an isometric view of a singleMRDD unit cell 10 containing a full MRDD structure along with radialstruts 31 that comprise portions of adjacent unit cells. FIG. 2 is aside view of a single MRDD unit cell 10 showing the configuration ofinterconnections when viewed from a lateral direction. A top or bottomview of the MRDD unit cell 10 would be substantially the same as theside view depicted in FIG. 2. The MRDD unit cell 10 differs in bothstructural characteristics and method of design from generic RDD shapes.A generic RDD is comprised of twelve faces where each face is anidentical rhombus with an acute angle of 70.5 degrees and an obtuseangle of 109.5 degrees. The shape of the rhombus faces in a generic RDDdo not change if the size of the unit cell or the diameter of the strutsare changed because the struts are indexed based on their axis and eachpass through the center of the fourteen nodes or vertices.

In some embodiments of the MRDD, each node 30 is contained within afixed volume that defines its bounds and provides a fixed point in spacefor the distal ends of the struts. The fixed volume containing the MRDDor a sub-unit cell of the MRDD can comprise of various shapes, includingbut not limited to, a cubic, cuboid, hexahedron or amorphous volume.Some examples use a fixed volume with six faces and eight cornersdefined by locations where three faces meet. The orientation of thestruts 31 can be based on the center of a node face at its proximate endand the nearest corner of the volume to that node face on its distalend. Each node 30 is preferably an octahedron, more specifically asquare bipyramid (i.e., a pyramid and inverted pyramid joined on ahorizontal plane). Each node 30, when centrally located in a cuboidvolume, more preferably comprises a square plane parallel to a face ofthe cuboid volume and six vertices. Each node 30 is oriented so thateach of the six vertices are positioned at their closest possiblelocation to each of the six faces of the cuboid volume. As used herein,the term “centrally located,” with regards to the node's location withina volume refers to positioning the node at a location substantiallyequidistant from opposing walls of the volume. In some embodiments, thenode 30 can have a volumetric density of 100%. In other embodiments, thenode 30 can have a volumetric density of less than 100%. Each face ofthe square bipyramid node 30 can be triangular and each face can providea connection point for a strut 31.

The struts 31 can also be octahedrons, comprising an elongate portion ofsix substantially similar elongate faces and two end faces. The elongatefaces can be isosceles triangles with a first internal angle, angle A,and a second internal angle, angle B, where angle B is greater thanangle A. The end faces can be substantially similar isosceles trianglesto one another with a first internal angle, angle C, and a secondinternal angle, angle D, where angle D is greater than angle C.Preferably, angle C is greater than angle A.

The strut direction of each strut is a line or vector defining theorientation of a strut and it can be orthogonal or non-orthogonalrelative to the planar surface of each node face. In the MRDD and radialdodeca-rhombus structures disclosed herein, the strut direction can bedetermined using a line extending between the center of the strut endfaces, the center of mass along the strut or an external edge or face ofthe elongate portion of the strut. When defining a strut direction usinga line extending between the center of the strut end faces, the line isgenerally parallel to the bottom face or edge of the strut. Whendefining a strut direction using a line extending along the center ofmass of the strut, the line can be nonparallel to the bottom face oredge of the strut. The octahedron nodes of the MRDD can be scaled toincrease or decrease volumetric density by changing the origin point andsize of the struts. The distal ends of the struts, however, are lockedat the fixed volume corners formed about each node so that their anglerelative to each node face changes as the volumetric density changes.Even as the volumetric density of an MRDD unit cell changes, thedimensions of the fixed volume formed about each node does not change.In FIG. 1, dashed lines are drawn between the corners of the MRDD unitcell 10 to show the cube 11 that defines its bounds. In the MRDD unitcell in FIG. 1, the height 12, width 13 and depth 14 of the unit cellare substantially the same, making the area defined by the cube 11.

In some embodiments, the strut direction of a strut 31 can intersect thecenter of the node and the corner of the cuboid volume nearest to thenode face where the strut 31 is fixed. In some embodiments, the strutdirection of a strut 31 can intersect just the corner of the cuboidvolume nearest to the node face where the strut is fixed. In someembodiments, a reference plane defined by a cuboid or hexahedron face isused to describe the strut direction of a strut. When the strutdirection of a strut is defined based on a reference plane, it can bebetween 0 degrees and 90 degrees from the reference plane. When thestrut direction of a strut is defined based on a reference plane, it ispreferably eight degrees to 30 degrees from the reference plane.

By indexing the strut orientation to a variable node face on one end anda fixed point on its distal end, the resulting MRDD unit cell can allowrhombus shaped faces with a smaller acute angle and larger obtuse anglethan a generic RDD. The rhombus shaped faces of the MRDD can have twosubstantially similar opposing acute angles and two substantiallysimilar opposing obtuse angles. In some embodiments, the acute anglesare less than 70.5 degrees and the obtuse angles are greater than 109.5degrees. In some embodiments, the acute angles are between 0 degrees and55 degrees and the obtuse angles are between 125 degrees and 180degrees. In some embodiments, the acute angles are between 8 degrees and60 degrees and the obtuse angles are between 120 degrees and 172degrees. The reduction in the acute angles increases fatigue resistancefor loads oriented across the obtuse angle corner to far obtuse anglecorner. The reduction in the acute angles and increase in obtuse anglesalso orients the struts to increase the MRDD's strength in shear andincreases the fatigue resistance. By changing the rhombus corner anglesfrom a generic RDD, shear loads pass substantially in the axialdirection of some struts, increasing the shear strength. Changing therhombus corner angles from a generic RDD also reduces overall deflectioncaused by compressive loads, increasing the fatigue strength byresisting deflection under load.

When placed towards the center of a lattice structure, the twelveinterconnections of a unit cell 30 connect to twelve different adjacentunit cells, providing continuous paths through the lattice. The size ofthe central void and interconnections in the MRDD may be defined usingthe longest dimension method as described herein. Using the longestdimension method, the central void can be defined by taking ameasurement of the longest dimension as demonstrated in FIG. 3. In FIG.3, the longest dimension is labeled as distance AA. The distance AA canbe taken in the vertical or horizontal directions (where the directionsreference the directions on the page) and would be substantially thesame in this example. The interconnections may be defined by theirlongest measurement when viewed from a side, top or bottom of a unitcell. In FIG. 4, the longest dimension is labeled as distance AB. Thedistance AB can be taken in the vertical or horizontal directions (wherethe directions reference the directions on the page). The view in FIG. 4is a lateral view, however, in this example the unit cell will appearsubstantially the same when viewed from the top or bottom.

The size of the central void and interconnections can alternatively bedefined by the largest sphere method as described herein. Using thelargest sphere method, the central void can be defined by the diameterof the largest sphere that can fit within the central void withoutintersecting the struts. FIG. 5 depicts an example of the largest spheremethod being used to define the size of a central void with a spherewith a diameter of BA. FIG. 6 is a view from a direction normal to theplanar direction of an interconnection being measured with the largestsphere method. The interconnections are generally rhombus shaped andtheir size can alternatively be defined by the size of the length andwidth of three circles drawn within the opening. As shown in FIG. 6,within the plane defining a side, a first circle BB1 is drawn at thecenter of the opening so that it is the largest diameter circle that canfit without intersecting the struts. A second circle BB2 and thirdcircle BB3 is then drawn so that they are tangential to the first circleBB1 and the largest diameter circles that can fit without intersectingthe struts. The diameter of the first circle BB1 is the width of theinterconnection and the sum of the diameters of all three circles BB1,BB2 & BB3 represents the length of the interconnection. Using thismethod of measurement removes the acute corners of the rhombus shapedopening from the size determination. In some instances, it is beneficialto remove the acute corners of the rhombus shaped opening from thecalculated size of the interconnections because of the limitations ofadditive manufacturing processes. For example, if an SLS machine has aresolution of 12 μm where the accuracy is within 5 μm, it is possiblethat the acute corner could be rounded by the SLS machine, making itunavailable for bone ingrowth. When designing lattices for manufactureon less precise additive process equipment, it can be helpful to usethis measuring system to better approximate the size of theinterconnections.

Using the alternative measuring method, in some examples, the width ofthe interconnections is approximately 600 μm and the length of theinterconnections is approximately 300 μm. The use of a 600 μm length and300 μm width provides an opening within the known pore sizes for bonegrowth and provides a surface area of roughly 1.8 square millimeters,allowing high strength bone growth to form. Alternative embodiments maycontain interconnections with a cross sectional area of 1.0 to 15.0times the cross-sectional area of a pore with a diameter of 300 μm.Other embodiments may contain interconnections with a cross sectionalarea of 1.0 to 15.0 times the cross-sectional area of a pore with adiameter of 900 μm.

The MRDD unit cell also has the advantage of providing at least two setsof substantially homogenous pore or opening sizes in a latticestructure. In some embodiments, a first set of pores have a width ofabout 200 μm to 900 μm and a second set of pores have a width of about 1to 15 times the width of the first set of pores. In some embodiments, afirst set of pores can be configured to promote the growth ofosteoblasts and a second set of pores can be configured to promote thegrowth of osteons. Pores sized to promote osteoblast growth can have awidth of between and including about 100 μm to 900 μm. In someembodiments, pores sized to promote osteoblast growth can have a widththat exceeds 900 μm. Pores sized to promote the growth of osteons canhave a width of between and including about 100 μm to 13.5 mm. In someembodiments, pores sized to promote osteon growth can have a width thatexceeds 13.5 mm.

In some embodiments, it is beneficial to include a number ofsubstantially homogenous larger pores and a number of substantiallyhomogenous smaller pores, where the number of larger pores is selectedbased on a ratio relative to the number of smaller pores. For example,some embodiments have one large pore for every one to twenty five smallpores in the lattice structure. Some embodiments preferably have onelarge pore for every eight to twelve smaller pores. In some embodiments,the number of larger and smaller pores can be selected based on apercentage of the total number of pores in a lattice structure. Forexample, some embodiments can include larger pores for 4% to 50% of thetotal number of pores and smaller pores for 50% to 96% of the totalnumber of pores. More preferably, some embodiments can include largerpores for about 8% to 13% of the total number of pores and smaller poresfor about 87% to 92% of the total number of pores. It is believed that alattice constructed with sets of substantially homogenous pores of thedisclosed two sizes provides a lattice structure that simultaneouslypromotes osteoblast and osteon growth.

The MRDD unit cell may also be defined by the size of theinterconnections when viewed from a side, top or bottom of a unit cell.The MRDD unit cell has the same appearance when viewed from a side, topor bottom, making the measurement in a side view representative of theothers. When viewed from the side, as in FIG. 4, an MRDD unit celldisplays four distinct diamond shaped interconnections withsubstantially right angles. The area of each interconnection is smallerwhen viewed in the lateral direction than from a direction normal to theplanar direction of each interconnection, but the area when viewed inthe lateral direction can represent the area available for bone to growin that direction. In some embodiments, it may be desirable to index theproperties of the unit cell and lattice based on the area of theinterconnections when viewed from the top, bottom or lateral directions.

In some embodiments of the lattice structures disclosed herein, thecentral void is larger than the length or width of the interconnections.Because the size of each interconnection can be substantially the samein a repeating MRDD structure, the resulting lattice can be comprised ofopenings of at least two discrete sizes. In some embodiments, it ispreferable for the diameter of the central void to be approximately twotimes the length of the interconnections. In some embodiments, it ispreferable for the diameter of the central void to be approximately fourtimes the width of the interconnections.

In some embodiments, the ratio between the diameter of the central voidand the length or width of the interconnections can be changed to createa structural lattice of a particular strength. In these embodiments,there is a correlation where the ratio between the central void diameterand the length or width of the interconnections increases as thestrength of the structural lattice increases.

It is also believed that a lattice using a repeating radialdodeca-rhombus (hereinafter “RDDR”) unit cell can present a preferablecombination of stiffness, strength, fatigue resistance, and conditionsfor bone ingrowth. In some embodiments, the repeating RDDR lattice iscomprised of titanium or a titanium alloy. FIG. 7 is an isometric viewof a single RDDR unit cell 20 containing a full RDDR structure. FIG. 8is a side view of a single RDDR unit cell 20 showing the configurationof interconnections when viewed from a lateral direction. A top orbottom view of the RDDR unit cell 20 would be substantially the same asthe side view depicted in FIG. 8.

As used herein, an RDDR unit cell 20 is a three-dimensional shapecomprised of a central node with radial struts and mirrored strutsthereof forming twelve rhombus shaped structures. The node is preferablyan octahedron, more specifically a square bipyramid (i.e. a pyramid andinverted pyramid joined on a horizontal plane). Each face of the node ispreferably triangular and fixed to each face is a strut comprised of sixtriangular facets and two end faces. The central axis of each strut canbe orthogonal or non-orthogonal relative to the planar surface of eachnode face. The central axis may follow the centroid of the strut. TheRDDR is also characterized by a central node with one strut attached toeach face, resulting in a square bipyramid node with eight strutsattached.

Examples of node and strut combinations are shown in FIGS. 9-13. FIG. 9depicts an isometric view of a single node 30 with a single strut 31attached. The node 30 is a square bipyramid oriented so that two peaksface the top and bottom of a volume 32 defining the bounds of the node30 and any attached strut(s) 31. The node 30 is oriented so that thehorizontal corners are positioned at their closest point to the lateralsides of the volume 32. The strut 31 extends from a node 30 face to thecorner of the volume 32 defining the bounds of the node and attachedstruts. In FIG. 9, the central axis of the strut 31 is 45 degrees abovethe horizontal plane where the node's planar face is 45 degrees above ahorizontal plane.

FIG. 9 also details an octahedron strut 31, where dashed lines showhidden edges of the strut. The strut 31 is an octahedron with anelongate portion of six substantially similar elongate faces and two endfaces. The elongate faces 31 a, 31 b, 31 c, 31 d, 31 e, and 31 f of thestrut 31 define the outer surface of the strut's elongate and somewhatcylindrical surface. Each of the elongate faces 31 a, 31 b, 31 c, 31 d,31 e, and 31 f is an isosceles triangle with a first internal angle,angle A, and a second internal angle, angle B, where angle B is greaterthan angle A. The strut 31 also has two end faces 31 f, 31 g which areisosceles triangles that are substantially similar to one another,having a first internal angle, angle C, and a second internal angle,angle D, and where angle D is greater than angle C. When comparing theinternal angles of the elongate faces 31 a, 31 b, 31 c, 31 d, 31 e, and31 f to the end faces 31 f and 31 g, angle C is greater than angle A.

In FIG. 10 is a side view of the node 30 and strut 31 combinationbounded by volume 32. In the side view, the height of the node 30compared to the height of the cube 32 can be compared easily. FIGS.11-13 depict side views of node and strut combinations viewed from acorner of the volume rather than a wall or face, and where thecombinations have been modified from FIGS. 9-10 to change the volumetricdensity of the resulting unit cell. FIG. 11, the height of the node 130has increased relative to the height of the volume 132. Since the distalend of the strut 131 is fixed by the location of a corner of the volume132, the strut 131 must change its angle relative to its attached nodeface so that it becomes non-orthogonal. The node 130 and strut 131combination, where the angle of the strut 131 from a horizontal plane isabout 20.6 degrees, would be appropriate for a lattice structure with anelastic modulus of approximately 3 GPa.

In FIG. 12, the height of the node 230 relative to the height of thecube 232 has been increased over the ratio of FIG. 11 to create a node230 and strut 231 combination that would be appropriate for a latticestructure with an elastic modulus of approximately 4 GPa. As the heightof the node 230 increases, the angle between the strut 231 and ahorizontal plane decreases to about 18.8 degrees. As the height of thenode 230 increases, the size of the node faces also increase so that thesize of the strut 231 increases. While the distal end of the strut 231is fixed to the corner of the volume 232, the size of the distal endincreases to match the increased size of the node face to maintain asubstantially even strut diameter along its length. As the node andstrut increase in size, the volumetric density increases, as does theelastic modulus. In FIG. 13, the height of the node 330 relative to theheight of the volume 332 has been increased over the ratio of FIG. 13 tocreate a node 330 and strut 331 combination that would be appropriatefor a lattice structure with an elastic modulus of approximately 10 GPa.In this configuration, the angle 333 between the strut 331 and ahorizontal plane decreases to about 12.4 degrees and the volumetricdensity increases over the previous examples. The single node and strutexamples can be copied and/or mirrored to create unit cells ofappropriate sizes and characteristics. For instance, the angle betweenthe strut and a horizontal plane could be increased to 25.8 degrees torender a lattice with a 12.3% volumetric density and an elastic modulusof about 300 MPa. While a single node and single strut were shown in theexamples for clarity, multiple struts may be attached to each node tocreate an appropriate unit cell.

Adjacent struts extending from adjacent node faces on either the upperhalf or lower half of the node have an angle from the horizontal planeand a lateral separation angle defined by an angle between the strutdirections of adjacent struts. In the MRDD and RDDR structures, adjacentstruts have an external edge or face of the elongate portion extendingclosest to the relevant adjacent strut. The lateral separation angle, asused herein, generally refers to the angle between an external edge orface of the elongate portion of a strut extending closest to therelevant adjacent strut. In some embodiments, a lateral separation angledefined by a line extending between the center of the strut end faces ora line defined by the center of mass of the struts can be used inreference to a similar calculation for an adjacent strut.

The lateral separation angle is the angle between the nearest face oredge of a strut to an adjacent strut. The lateral separation angle canbe measured as the smallest angle between the nearest edge of a strut tothe nearest edge of an adjacent strut, in a plane containing both strutedges. The lateral separation angle can also be measured as the anglebetween the nearest face of a strut to the nearest face of an adjacentstrut in a plane normal to the two strut faces. In embodiments withoutdefined strut edges or strut faces, the lateral separation angle can bemeasured as an angle between the nearest portion of one strut to thenearest portion of an adjacent strut. For a unit cell in a cubic volume,as the strut angle from the horizontal plane decreases, the lateralseparation angle approaches 90 degrees. For a unit cell in a cubicvolume, as the strut angle from the horizontal plane increases, thelateral separation angle approaches 180 degrees. In some embodiments, itis preferable to have a lateral separation angle greater than 109.5degrees. In some embodiments, it is preferable to have a lateralseparation angle of less than 109.5 degrees. In some embodiments, it ispreferable to have a lateral separation angle of between and includingabout 108 degrees to about 156 degrees. In some embodiments, it is morepreferable to have a lateral separation angle of between and including111 degrees to 156 degrees. In some embodiments, it is more preferableto have a lateral separation angle of between and including 108 degreesto 120 degrees. In some embodiments, it is most preferable to have alateral separation angle of between and including about 111 degrees to120 degrees. In some embodiments, it is more preferable to have alateral separation angle of between and including 128 degrees to 156degrees. FIG. 14 depicts a side view, viewed from a corner of the cube432, of a single node 430 with two adjacent struts 431, 434 attached,and where the lateral separation angle 443 is identified. When measuredfrom the nearest edge of a strut to the nearest edge of an adjacentstrut, the lateral separation angle 443 is about 116 degrees.

In some embodiments, a unit cell is built up from multiple sub-unitcells fixed together. FIG. 15 depicts an isometric view of an exemplarysub-unit cell comprising a single node and four struts. FIG. 16 depictsan isometric view of two sub-unit cells in a stacked formation where theupper sub-unit cell is inverted and fixed to the top of the lowersub-unit cell. FIG. 17 depicts an isometric view of eight sub-unit cellsstacked together to form a single RDDR unit cell.

In FIG. 15, the node 530 is a square bipyramid, oriented so that the twopeaks face the top and bottom of a cubic volume 532. In someembodiments, the volume 532 can be a cuboid volume, a hexahedron volume,an amorphous volume or of a volume with one or more non-orthogonalsides. The peaks refer to the point where four upper faces meet and thepoint where four lower faces meet. The node 530 is oriented so that thehorizontal vertices face the lateral sides of the cubic volume 532. Thestrut 531 is fixed to a lower face of the node 530 face on its proximateend and extends to the nearest corner of the cubic volume 532 at itsdistal end. The distal end of the strut 531 can remain fixed to thecubic volume 532 even if the node 530 changes in size to adjust thesub-unit cell properties.

On the lower face of the node 530 opposite the face which strut 531 isfixed, the proximate end of strut 534 is fixed to the node 530. Thestrut 534 extends to the nearest corner of cubic volume 532 at itsdistal end. The strut 535 is fixed on its proximate end to an upper node530 face directed about 90 degrees laterally from the node B530 facefixed to strut 531. The strut 535 extends to the nearest corner of thecubic volume 532 at its distal end. On the upper face of the node 530opposite the face which strut 535 is fixed, the proximate end of strutB536 is fixed to the node 530. The strut 536 extends to the nearestcorner of the cubic volume 532 at its distal end.

In some embodiments, the struts 531, 534-536 are octahedrons withtriangular faces. The strut face fixed to a node 530 face can besubstantially the same size and orientation of the node 530 face. Thestrut face fixed to the nearest corner of the cube 532 can besubstantially the same size as the strut face fixed to the node 530 andoriented on a substantially parallel plane. The remaining six faces canbe six substantially similar isosceles triangles with a first internalangle and a second internal angle larger than said first internal angle.The six substantially similar isosceles triangles can be fixed alongtheir long edges to an adjacent and inverted substantially similarisosceles triangle to form a generally cylindrical shape with triangularends.

When forming a sub-unit cell 540, it can be beneficial to add an eighthnode 538 to each corner of the cube 532 fixed to a strut 531, 534-536.When replicating the sub-unit cell 540, the eighth node 538 attached toeach strut end is combined with eighth nodes from adjacent sub-unitcells to form nodes located between the struts of adjacent sub-unitcells.

FIG. 16 is a first sub-unit cell 540 fixed to a second sub-unit cell 640to form a quarter unit cell 560 used in some embodiments. The secondsub-unit cell 640 comprises a square bipyramid node 630 is a squarebipyramid, oriented so that the two peaks face the top and bottom of acubic volume. The node 630 is oriented so that the horizontal verticesface the lateral sides of the cubic volume. The strut 635 is fixed to alower face of the node 630 face on its proximate end and extends to thenearest corner of the cubic volume at its distal end. On the lower faceof the node 630 opposite the face which strut 635 is fixed, theproximate end of strut 636 is fixed to the node 630. The strut 636extends to the nearest corner of cubic volume at its distal end. Thestrut 634 is fixed on its proximate end to an upper node 630 facedirected about 90 degrees laterally from the node 630 face fixed tostrut 635. The strut 634 extends to the nearest corner of the cubicvolume at its distal end. On the upper face of the node 630 opposite theface which strut 634 is fixed, the proximate end of strut 631 is fixedto the node 630. The strut 631 extends to the nearest corner of thecubic volume at its distal end.

The first sub-unit 540 is used as the datum point in the embodiment ofFIG. 16, however, it is appreciated that the second sub-unit cell 640 oranother point could also be used as the datum point. Once the firstsub-unit cell 540 is fixed in position, it is replicated so that thesecond sub-unit cell 640 is substantially similar to the first. Thesecond sub-unit cell 640 is rotated about its central axis prior tobeing fixed on the top of the first unit-cell 540. In FIG. 16, thesecond sub-unit cell 640 is inverted to achieve the proper rotation,however, other rotations about the central axis can achieve the sameresult. The first sub-unit cell 540 fixed to the second sub-unit cell640 forms a quarter unit cell 560 that can be replicated and attachedlaterally to other quarter unit cells to form a full unit cell.

Alternatively, a full unit cell can be built up by fixing a first groupof four substantially similar sub-unit cells together laterally to forma square, rectangle or quadrilateral when viewed from above. A secondgroup of four substantially similar sub-unit cells rotated about theircentral axis can be fixed together laterally to also form a square,rectangle or quadrilateral when viewed from above. The second group ofsub-unit cells can be rotated about their central axis prior to beingfixed together laterally or inverted after being fixed together toachieve the same result. The second group is then fixed to the top ofthe first group to form a full unit cell.

FIG. 17 is an example of a full unit cell 770 formed by replicating thesub-unit cell 540 of FIG. 15. The cube 532 defining the bounds of thesub-unit cell 540 is identified as well as the node 530 and struts 531,534-536 for clarity. The full unit cell 770 of FIG. 17 can be formedusing the methods described above or using variations within theinventive concept.

Each strut extending from the node, for a given unit cell, can besubstantially the same length and angle from the horizontal plane,extending radially from the node. At the end of each strut, the strut ismirrored so that struts extending from adjacent node faces form arhombus shaped opening. Because the struts can be non-orthogonal to thenode faces, rhombuses of two shapes emerge. In this configuration, afirst group of four rhombuses extend radially from the node oriented invertical planes. The acute angles of the first group of rhombuses equaltwice the strut angle from the horizontal plane and the obtuse anglesequal 180 less the acute angles. Also in this configuration is a secondgroup of eight rhombuses extending radially so that a portion of thesecond group of eight rhombuses fall within the lateral separation anglebetween adjacent struts defining the first group of four rhombuses. Theacute angles of the second group of rhombuses can be about the same asthe lateral separation angle between adjacent struts that define thefirst group of four rhombuses and the obtuse angles equal 180 less theacute angles. The characteristics of a scaffold may also be described byits surface area per volume. For a 1.0 mm×1.0 mm×1.0 mm solid cube, itssurface area is 6.0 square mm. When a 1.0 cubic mm structure iscomprised of a lattice structure rather than a 100% volumetric densitymaterial, the surface area per volume can increase significantly. In lowvolumetric density scaffolds, the surface area per volume increases asthe volumetric density increases. In some embodiments, a scaffold with avolumetric density of 30.1% would have a surface area of 27.4 square mmper cubic mm. In some embodiments, if the volumetric density wasdecreased to 27.0%, the lattice would have a surface area of 26.0 squaremm per cubic mm and if the volumetric density were decreased to 24.0%,the lattice would have a surface area of 24.6 square mm per cubic mm.

The MRDD and RDDR structures disclosed herein also have the advantage ofan especially high modulus of elasticity for a given volumetric density.When used as a lattice or scaffold, an implant with an adequate modulusof elasticity and a low volumetric density can be achieved. A lowvolumetric density increases the volume of the implant available forbone ingrowth.

In Table 1, below, are a number of example lattice configurations ofvarious lattice design elastic moduli. An approximate actual elasticmodulus was given for each example, representing a calculated elasticmodulus for that lattice after going through the manufacturing process.The lattice structures and implants disclosed herein can be designed toa design elastic modulus in some embodiments and to an approximateactual elastic modulus in other embodiments. One advantage of thepresently disclosed lattice structures is that the approximate actualelastic modulus is much closer to the design elastic modulus than hasbeen previously achieved. During testing, one embodiment of a latticewas designed for a 4.0 GPa design elastic modulus. Under testing, thelattice had an actual elastic modulus of 3.1 GPa, achieving an actualelastic modulus within 77% of the design elastic modulus.

For each lattice design elastic modulus, a volumetric density, ratio ofdesign elastic modulus to volumetric density, surface area in mm², ratioof surface area to volumetric density and ratio of surface area tolattice design elastic modulus is given.

TABLE 1 Table of example lattice structures based on lattice designelastic modulus in GPa Ratio of Ratio of Design Ratio of Surface LatticeApprox. Elastic Surface Area Design Actual Volu- Modulus Area to toLattice Elastic Elastic metric to Volu- Surface Volu- Design ModulusModulus Density metric Area metric Elastic (GPa) (GPa) (percent) Density(mm²) Density Modulus 0.3 0.233 18.5 1.6 22.5 121.5 74.9 3 2.33 29.910.0 27.5 92.2 9.2 4 3.10 33.4 12.0 28.8 86.4 7.2 5 3.88 36.4 13.8 29.982.2 6.0 6 4.65 38.8 15.5 30.7 79.1 5.1 7 5.43 40.8 17.2 31.3 76.9 4.5 86.20 42.1 19.0 31.8 75.4 4.0 9 6.98 43.2 20.8 32.1 74.3 4.0

In some of the embodiments disclosed herein, the required strutthickness can be calculated from the desired modulus of elasticity.Using the following equation, the strut thickness required to achieve aparticular elastic modulus can be calculated for some MRDD and RDDRstructures:Strut Thickness=(−0.0035*(E{circumflex over ( )}2))+(0.0696*E)+0.4603

In the above equation, “E” is the modulus of elasticity. The modulus ofelasticity can be selected to determine the required strut thicknessrequired to achieve that value or it can be calculated using apreselected strut thickness. The strut thickness is expressed in mm andrepresents the diameter of the strut. The strut thickness may becalculated using a preselected modulus of elasticity or selected todetermine the modulus of elasticity for a preselected strut thickness.

In some embodiments, the unit cell can be elongated in one or moredirections to provide a lattice with anisotropic properties. When a unitcell is elongated, it generally reduces the elastic modulus in adirection normal to the direction of the elongation. The elastic modulusin the direction of the elongation is increased. It is desirable toelongate cells in the direction normal to the direction of new bonegrowth contained within the interconnections, openings and central voids(if any). By elongating the cells in a direction normal to the desireddirection of reduced elastic modulus, the shear strength in thedirection of the elongation may be increased, providing a desirable setof qualities when designing a structural scaffold. Covarying the overallstiffness of the scaffold may augment or diminish this effect, allowingvariation in one or more directions.

In some embodiments, the sub-unit cells may be designing by controllingthe height of the node relative to the height of the volume that definesthe sub-unit cell. Controlling the height of the node can impact thefinal characteristics and appearance of the lattice structure. Ingeneral, increasing the height of the node increases the strutthickness, increases the volumetric density, increases the strength andincreases the elastic modulus of the resulting lattice. When increasingthe height of the node, the width of the node can be held constant insome embodiments or varied in other embodiments.

In some embodiments, the sub-unit cells may be designing by controllingthe volume of the node relative to the volume that defines the sub-unitcell. Controlling the volume of the node can impact the finalcharacteristics and appearance of the lattice structure. In general,increasing the volume of the node increases the strut thickness,increases the volumetric density, increases the strength and increasesthe elastic modulus of the resulting lattice. When increasing the volumeof the node, the width or height of the node could be held constant insome embodiments.

In Table 2, below, are a number of example lattice configurations ofvarious lattice design elastic moduli. An approximate actual elasticmodulus was given for each example, representing a calculated elasticmodulus for that lattice after going through the manufacturing process.The lattice structures and implants disclosed herein can be designed toa design elastic modulus in some embodiments and to an approximateactual elastic modulus in some embodiments. For each lattice designelastic modulus, a lattice approximate elastic modulus, a node height, avolumetric density, a node volume, a ratio of node height to volumetricdensity, a ratio of node height to lattice design elastic modulus and aratio of volumetric density to node volume is given.

TABLE 2 Table of example lattice structures based on lattice designelastic modulus in GPa Ratio of Lattice Node Ratio Lattice Approx. Volu-Ratio Height of Vol. Design Actual metric of to Den- Elastic ElasticDen- Node Node Lattice sity to Mod- Mod- Node sity Vol- Height DesignNode ulus ulus Height (per- ume to Vol. Elastic Vol- (GPa) (GPa) (mm)cent) (mm3) Density Modulus ume 0.30 0.23 0.481 18.5 0.0185 2.60 1.609.98 3.00 2.33 0.638 29.9 0.0432 2.14 0.21 6.91 4.00 3.10 0.683 33.40.0530 2.05 0.17 6.29 5.00 3.88 0.721 36.4 0.0624 1.98 0.14 5.82 6.004.65 0.752 38.8 0.0709 1.94 0.13 5.48 7.00 5.43 0.776 40.8 0.0779 1.900.11 5.23 8.00 6.20 0.793 42.1 0.0831 1.88 0.10 5.07 9.00 6.98 0.80743.2 0.0877 1.87 0.09 4.93

Some embodiments of the disclosed lattice structures are particularlyuseful when provided within an elastic modulus range between anincluding 0.375 GPa to 4 GPa. Some embodiments, more preferably, includea lattice structure with an elastic modulus between and including 2.5GPa to 4 GPa. Some embodiments include a lattice structure with avolumetric density between and including 5% to 40%. Some embodiments,more preferably, include a lattice structure with a volumetric densitybetween and including 30% to 38%.

The lattice structures disclosed herein have particularly robust loadingand fatigue characteristics for low volumetric density ranges and lowelastic moduli ranges. Some embodiments of the lattice structures have ashear yield load and a compressive yield load between and including 300to 15000N in static and dynamic loading up to 5,000,000 cycles at 5 Hz.Some embodiments have a compressive shear strength and an axial loadbetween and including 300 to 15000N in static and dynamic loading up to5,000,000 cycles at 5 Hz. Some embodiments have a shear strength and anaxial load between and including 300 to 15000N in static and dynamicloading up to 5,000,000 cycles at 5 Hz. Some embodiments have atorsional yield load up to 15 Nm.

In one example, the inventive lattice structure has a volumetric densityof between and including 32% to 38%, an elastic modulus between andincluding 2.5 GPa to 4 GPa and a shear strength and an axial loadbetween and including 300 to 15000N in static and dynamic loading up to5,000,000 cycles at 5 Hz. Some examples include a first set ofsubstantially homogeneous openings with a width of about 200 μm to 900μm and a second set of substantially homogenous openings with a width ofabout 1 to 15 times the width of the first set of openings, where thenumber of openings in the second set are provided at a ratio of about1:8 to 1:12 relative to the number of openings in the first set.

The disclosed structures can also have benefits when used inapplications where osteointegration is not sought or undesirable. Byincluding a growth inhibiting coating or skin on a structure, thelattice disclosed herein can be used to provide structural supportwithout providing a scaffold for bone growth. This may be desirable whenused in temporary implants or medical devices that are intended to beremoved after a period of time.

In some embodiments presented herein relate to a biocompatible latticewith increased lucency, a method of designing a lattice with increasedlucency, variable markers for use in medical implants with at least adegree of radiolucency, a method of designing variable markers for usein medical implants with at least a degree of radiolucency and a methodof using variable markers in medical implants with a degree ofradiolucency. Variable markers, as used herein, refers to any area of animplant that has a different lucency, radiolucency, radiopacity orradiodensity in at least two different viewing directions. Variablemarkers can have one or more aligned directions, meaning a directionwhere the variable markers are designed to produce a specific lucency,radiolucency, radiopacity or radiodensity. Variable markers can have oneor more misaligned directions, meaning directions where the variablemarkers are designed to produce a different lucency, radiolucency,radiopacity or radiodensity in comparison to an aligned direction. Thevariable markers can be configured to provide either increased lucencyor decreased lucency when viewed in an aligned direction in comparisonto when viewed in a misaligned direction. In some embodiments, thelattice structures with increased lucency include variable markers. Onlyexemplary embodiments are shown herein and it is understood that the useof other unit cell structures, other lattice structures and other porousstructures would be within the inventive concept expressed herein. Thedirections described herein are in relation to the three-dimensionalCartesian Coordinate System where the x axis and y axes are horizontaland the z axis is vertical (also described herein as the x, y and z“direction”). These specific directional references are exemplary andused to the example orientations described herein.

Biocompatible lattices can be comprised of a material that hasradiopaque properties when a certain bulk thickness is reached. In thiscase, bulk thickness means the actual thickness of the primary materialin a lattice in a certain direction when the voids are removed. Forinstance, a lattice with a 50% volumetric density and a thickness of twoinches would have a bulk thickness of one inch in that direction and alattice with a 25% volumetric density and a thickness of two incheswould have a bulk thickness of a half inch in that direction.

As used herein, radiodensity refers to the opacity or lucency of amaterial when viewed in in an x-ray or similar process. The radiodensityof a material may range from radiopaque to radiolucent. Radiopaque meansthat the material completely blocks the transmission of x-rays. Aradiopaque material would show up as white in most x-rays. Radiolucentmeans that the material does not block the transmission of x-rays orblocks less than all of the x-rays. A fully radiolucent material wouldshow up as black on most x-rays. A partially radiolucent material wouldshow up as gray in most x-rays. As a material becomes more radiolucent,it shows up progressively darker in an x-ray.

FIG. 18 depicts an exemplary embodiment of the inventive lattice thatuses a repeating cubic unit cell structure. The example in FIG. 18 hasbeen rotated 23 degrees about the z axis and 33.67 degrees about the xaxis from a normal face to provide increased dispersion. The angles ofrotation about the x, y and z axes are relative to an origin orientationfor a single unit cell or a structure comprised of a plurality of unitcells. In the cubic cell example, the origin orientation is where onecell face is within the plane defined by the x and z axes, another cellface is within the plane defined by the y and z axes and another cellface is within the plane defined by the x and y axes. When a cubic cellis positioned in this particular origin orientation, the rotation of thecubic cell may also be described as an angle of rotation from a normalface. Because the origin orientation is used as a reference point forthe rotations taught herein, the exemplary rotations disclosed wouldchange accordingly if a different origin orientation were used as areference.

When using a repeating geometric unit cell in a lattice, depending onthe orientation of the unit cells, the degree of lucency and the type oflucency (e.g. dispersion or disparity) through the material can bemodified. While many types of lucency may be targeted using the methodsdescribed herein, only the maximum relative disparity and maximumrelative dispersion angles will be discussed in detail. The maximumrelative disparity angles are the rotations in degrees about the x, yand z axes for a certain repeating geometric unit cell that provides themaximum difference in lucency across the bulk volume. The maximumdisparity angles result in an open cell structure with the highestpossible difference between the maximum bulk thickness and minimum bulkthickness in the desired direction, in other words, a minimum uniformityof bulk thickness. The maximum relative dispersion angles are therotations in degrees about the x, y and z axes for a certain repeatinggeometric unit cell that provides the minimum difference in lucencyacross the bulk volume. The maximum dispersion angles result in an opencell structure with the lowest possible difference between the maximumbulk thickness and minimum bulk thickness in the desired direction, inother words, a maximum uniformity of bulk thickness.

The average bulk thickness is an average taken of the bulk thicknessacross the bulk volume in the desired direction. For increased lucency,it is desirable to have a lower average bulk thickness in the desireddirection. When orienting a structure for the maximum dispersion angle,it can be beneficial to optimize the rotation angles to create astructure with a minimum average bulk thickness and maximum uniformityof the bulk thickness in the desired direction. While a minimum averagebulk thickness is desirable for lucency, the average bulk thickness in adesired direction is largely a function of the strut and unit cellcharacteristics. However, there can be a measurable reduction in averagebulk thickness when certain types of unit cell structures with struts ofcertain dimensions are rotated. The reduction in average bulk thicknessresulting from a rotation is more pronounced in simpler unit cellstructures, such as a triangular unit cell.

The desired direction, when used to describe the embodiments, is thedirection from which a lucency property is desired. Most of the time,the desired direction for a lucency property will be the direction fromwhich an x-ray image will be taken. For example, in a spinal interbodyimplant, x-ray imaging is usually taken from the lateral oranterior-posterior directions. In this case, the desired direction wouldbe from the lateral or anterior-posterior direction as the implant sitsin vivo. In the drawings disclosed herein, the desired direction can bea direction normal to the sheet or screen upon which the drawings aredepicted.

The repeating geometric pattern in FIG. 18 has been rotated to increasedispersion in the desired direction. For a repeating cubic unit cell,maximum relative dispersion is best achieved through the use of at leasttwo rotations, in this case about the z and x axes. When oriented inaccordance with FIG. 18, there is a minimal amount of overlap betweenthe struts and the nodes in the sample do not overlap at all. This is anexample of the maximization of uniformity of bulk thickness achievablein dispersion. Partial dispersion can be achieved with either rotationindividually, but would result in either horizontal or vertical lines ofdisparity.

As the overall thickness of the open cell scaffold increases, more cellsmay be added and nodes and struts will begin to overlap, increasing thebulk thickness of the structure. The optimal angles for maximumdispersion and minimal bulk thickness will vary with the overall numberof cells in the structure.

Additionally, the actual maximum dispersion depends on the ratio betweenthe diameter of the struts compared to the size of the unit cell. Asstrut diameter approaches the overall size of the unit cell, effectivelyclosing off the cells, there is no rotation that would substantiallyminimize bulk thickness. However, as the aspect ratio decreases, arotation can again achieve the offsetting of struts to minimize bulkthickness. The aspect ratio is the ratio between the strut thickness andstrut length. The aspect ratio can be decreased by, for example,increasing the strut length in the case of thick struts.

As an example, in a 2.0 mm cubic unit cell (where the dimensions in thex, y and z axes are 2.0 mm) with struts of 0.5 mm diameter, the centralvoid is approximately 1.0 mm in width and height. By rotating this unitcell and aligning each strut with a central void, the bulk thickness canbe approximately halved. As the struts in this example are increased indiameter, the impact of the rotation is reduced.

FIG. 19 depicts an exemplary embodiment of the inventive lattice using acubic unit cell and rotated to a different orientation. In FIG. 19, thelattice has been rotated 22 degrees about the z axis and 30 degreesabout the x axis from an origin orientation normal to a cubic unit cellface. Even with less of a rotation about the x and z axis than in FIG.18, the embodiment of FIG. 19 still maintains a similar dispersioneffect with minimal overlap of nodes and struts.

High disparity embodiments can be achieved through a variety of rotationcombinations. FIG. 20 depicts an exemplary embodiment of a lattice ofcubic unit cells where the lattice has been rotated 45 degrees about thez axis and 45 degrees about the x axis from an origin orientation normalto a cubic unit cell face. FIG. 21 depicts an exemplary embodiment of alattice of cubic unit cells where the lattice has been rotated 45degrees about the x axis from an origin orientation normal to a cubicunit cell face. FIG. 25 depicts an exemplary embodiment of a lattice ofcubic unit cells where the lattice has not been rotated from an originorientation normal to a cubic unit cell face. All of the high relativedisparity embodiments are characterized by significant overlap betweenthe nodes and struts of the unit cells. The significant overlapincreases the bulk thickness of the structure at certain points in thedesired direction, increasing radiopacity in those areas. The highrelative disparity embodiments also have areas where no struts or nodesobscure visibility through the structure, increasing the radiolucency inthose areas.

A diamond cubic cell has two interpenetrating face centered Bravaislattices within a cubic cell, wherein the Bravais lattices are shiftedalong a diagonal of the cubic cell by one quarter of the diagonallength. For a single diamond cubic unit cell in an origin orientationwhere three cubic faces are aligned with the x, y and z axes,respectively, the maximum relative disparity in the desired directioncan be achieved when the unit cell is rotated approximately 45 degreesabout the z axis from the origin orientation. In some embodiments of asingle diamond cubic unit cell in an origin orientation where threecubic faces are aligned with the x, y and z axes, respectively, themaximum relative disparity in the desired direction can be achieved whenthe unit cell is rotated approximately 45 degrees about the x axis or yaxis from the origin orientation. For the same single diamond cubic unitcell, relative maximum dispersion can be achieved at approximately 0 and90° rotations from the origin orientation. The origin orientation canalso be measured relative to a planar face of the cubic cell.

For a single lattice unit cell comprising a repeating generic RDD, MRDDor RDDR structure in an origin orientation where three cubic faces arealigned with the x, y and z axes, respectively, the maximum relativedispersion in the desired direction can occur when the structure isrotated approximately 45 degrees about the z axis from the originorientation. In some embodiments of a single lattice unit cellcomprising a repeating generic RDD, MRDD or RDDR structure in an originorientation where three cubic faces are aligned with the x, y and zaxes, respectively, the maximum relative dispersion in the desireddirection can occur when the structure is rotated approximately 45degrees about the x axis or y axis from the origin orientation. Themaximum relative disparity in the desired direction can occur when thesingle unit cell structure is not rotated at all (0°). While only sometypes of unit cell structures have been disclosed, there are many typesof repeating unit cell structures that can be used to achieve similarresults. Possible scaffold geometries that are appropriate include, butare not limited to, rhombic dodecahedron, diamond, dodecahedron, square,pentagonal, hexagonal, octagonal, sctet struts, trunic octa, diagonalstruts, other known geometric structures, and rounded or reinforcedversions of each geometry. The rotation along the x, y or z axes may bedifferent for different unit cell shapes and materials and can bedetermined based on the disclosure herein. The amount of rotation aboutthe x, y or z axes will also depend on the aspect ratio of the unitcells and the number of unit cells comprising the structure. As thenumber of unit cells increases, the nodes and struts will overlap, butthrough rotating the structure, the overlap of the nodes and struts maybe optimized. The use of rounded or reinforced nodes would increase theamount of material present near the nodes, increasing the bulk thicknessover areas where the nodes are present. The origin orientation can alsobe measured relative to a planar face of the cubic cell.

Rotations of structures may be represented relative to a base referenceframe or as Euler angles in a reference frame, preferably in aright-hand reference frame about the x, y, and z axes and composed in arotation matrix. Additional translation of the lattice structure may beachieved in the same step by expanding the matrix. While a Cartesiancoordinate system is used as an example reference frame or coordinatesystem, other reference frames could be appropriate and could be moreefficient, depending on the structure being analyzed.

These angles are determined based on the aspect ratios and geometries ofthe particular lattice structure. Specifically, the strut diameter, cellheight, cell width, cell depth, and overall thickness, length, andheight of the device are key parameters for solving rotation angles inx, y, and z axes, according to the following:R(x,y,z,α,β,γ)=F(h,w,d,T,H,L)

Where:

d=Strut diameter

h=Cell height

w=Cell width

d=Cell depth

T=Device Thickness

H=Device Height

L=Device Length

In some embodiments, the rotation of a structure can be referred tobased on a rotation in degrees about an axis. The high x-ray lucencystructures disclosed herein, in some embodiments, are achieved byrotating the structure from an origin orientation between and includingzero degrees to 180 degrees in either direction about an axis. In someembodiments, the high x-ray lucency structures are achieved by rotatingthe structure from an origin orientation between and including zerodegrees to 360 degrees about an axis. In some embodiments, the highx-ray lucency structures are achieved by rotating the structure from anorigin orientation between and including 35 degrees to 55 degrees ineither direction about an axis.

Some examples of lattices comprising repeating geometric unit cells thathave been optimized for lucency were disclosed above, but the methodused to design the exemplary embodiments can be applied to unit cells ofother specifications using a manual or computer aided method disclosedherein. The method of optimizing a structure for lucency is describedherein as a method of design and manufacture. The method of optimizing astructure for lucency disclosed herein can be applied to many types ofstructures, including but not limited to, lattice structures withrepeating geometric patterns and porous structures with either repeatingstructures or random structures. While the methods disclosed generallydesign the orientation of the lattice first and then produce the latticein a method of manufacture, the steps could just as easily be reversed.A lattice may be first manufactured and then oriented using the methodof design. For instance, a lattice may be first manufactured and then,by using the characteristics of the manufactured structure, a user mayuse the method of design to orient the structure for a lucency quality.The lattice could then be rotated to that orientation and cut, machinedor formed into its final shape.

The method of design can be performed through a manual process either bymanufacturing a structure and performing evaluations on a physical modelor performed in a software that generates the structure within aspecified volume of the implant at a user-defined unit cell orientationand then displays the result for visualization. In a first exemplarymethod of design, the user iterates the process, changing theorientation parameters for the unit cell, regenerating the structure,assessing the achieved bulk thickness of the device, and the uniformityof that thickness across the implant. Once the user is satisfied withthe minimally achieved bulk thickness and its uniformity, the parametersand final structure is accepted. Computer aided design (hereinafter“CAD”) or other three-dimensional (hereinafter “3D”) models of the unitcell structure can also be used as a starting point to identify optimalrotations or starting points.

The method of design can also be performed using a process aided withalgorithms and visualizations tools. In a second exemplary method ofdesign, a user would:

1. Generate or import a bulk volume repeating structure in a formcapable of analysis by an analysis tool. An analysis tool, as usedherein, refers to any application or process used to analyze data. Ananalysis tool could be an application or program capable of analyzingmultiple variables, such as MATLAB®, FreeMat, Octave, Mathematica®, orany comparable or custom software. The analysis tool may comprise adifferent program, comprise a user generated program or comprise anyother program, device, person or persons capable of analyzing multiplevariables. The analysis tool can also be one or more people visuallyanalyzing a repeating structure. The form capable of analysis isdifferent for each type of analysis tool available. For example, in anapplication or program, the repeating structure would likely need to beimported or a facsimile created within the capabilities of theapplication or program. If the analysis tool is a person, one formcapable of analysis would be a manufactured repeating unit cellstructure.

2. Propagate the bulk volume at some orientation throughout the specificdevice volume or perform on a raw structure independent of specificdevice constraints. The bulk volume can alternatively be sectioned tothe appropriate dimensions of a selected implant type.

3. Determine the uniformity of the bulk thickness from a desireddirection. The uniformity of bulk thickness can be determined throughmultiple methods, including by measuring the bulk thicknesses across thebulk volume in the desired direction(s) for viewing and then calculatingthe uniformity of bulk thickness. In some methods, the bulk thicknessesmay be visualized as a 2D heat map of the structure in the desireddirection(s). In some methods, the coefficient of determination (R²)would be a good indicator of the uniformity of bulk thickness.

4. Iterate across rotations of the bulk volume to identify the desireduniformity.

5. The parameters are captured, and a final structure is generated.

This method of design does not need to be performed in the precise orderdescribed above and may also be automated. A first possibility is simplyby performing all possible combinations of angle rotations in a MonteCarlo simulation. A second, by applying artificial intelligence andmachine learning algorithms (k-means, regression, Support VectorMachines, neural networks, or other such techniques) to achieve theoptimal angle of rotation for a specific structure.

The methods of increasing lucency of implants can also include the stepof selecting a focal length to determine a region of interest on animplant. The focal length, as used herein, refers to the expecteddistance between an imaging device and the implant during imaging duringor after implantation. Many x-rays are taken from a focal length ofabout 2-2.5 feet, but this distance could be adjusted to accommodate aparticular x-ray machine that deviates from the usual distance. In manyx-ray machines, a distance of about 5 feet is used between an x-rayemitter and receiver, with a patient located about an equal distancefrom the emitter and receiver. The x-ray emitter is commonly movedrelative to a patient to chance the field of view or amount of detail inthe x-ray image. The focal length helps identify a specific area ofinterest in the implant for imaging. When imaging is taken with anemitter about 2-2.5 feet away from a patient, the area of interest canbe more lucent than the remainder of the implant due to the viewingangle of the x-ray machine.

In some methods, an infinite focal length can be used to determine theoptimal lucency property angle for an entire side of an implant. In somemethods, where a focal length of some value is used, the implant canhave a rotation gradient to provide an even lucency effect, even with afocal length of less than infinite. A rotation gradient could beprovided with a lattice that rotated the unit cells relative to the unitcell orientation around a focal point. The rotation gradient couldcompensate for x-ray machines with a particularly short focal length orto maximize the imaging area. A maximized imaging area could be usefulto provide a broader image of the implant during and after implantation.A maximized imaging area could also be useful to display internalserialization, numerals, letters, or identification patterns (e.g., abarcode or a matrix barcode) over a broad area of an implant.

These algorithms can be expanded further to include variations of theunit cell size and strut thickness within specified constraints tofurther optimize the structure. Such constraints may include boundedranges on each parameter, overall device volumetric density, constructstiffness, or other relational conditions between or external to theseparameters.

In a third exemplary method of design, a user would:

1. Choose a repeating geometric structure and material that meets thestructural requirements.

2. Pick an origin orientation for a bulk volume comprising the selectedrepeating geometric structure and material.

3. Run a multivariable analysis for uniformity of bulk volume from thedesired direction(s) where the structure is rotated from its originorientation by at least 90 degrees along the x, y and z axes. In casesof asymmetry, it may be necessary to rotate in the positive and negativedirections about each axis (e.g. a rotation of 90 degrees and −90degrees about an axis). In unit cells where a reduction in average bulkthickness can be achieved through a rotation, it can be beneficial torun a multivariable analysis for average bulk thickness as well.

4. Use the multivariable analysis to determine the rotation from theorigin orientation that produces desirable lucency characteristics inthe desired direction(s) (i.e. dispersion).

This method of design represents a series of steps that may be taken tooptimize a preselected repeating geometric lattice structure for lucencyin a desired direction. These steps do not need to be taken in order andadditional variables may be considered before, after or during themethod of design to optimize a repeating geometric lattice for aparticular application. For example, the method of design could includethe cell size or strut thickness as variables rather than an input valuein the first step, or account for structures with variable cell size orstrut thickness. Other variables or constraints may also be consideredwithin this method of design.

In some embodiments, voids may be included within the implant to reducethe bulk thickness in the desired direction. Generally, a lower bulkthickness is better for lucency and the inclusion of voids in thedesired direction can reduce the bulk thickness in that direction.

The use of the above disclosed lattice and method of design can also beused to design variable markers in some embodiments. Variable markers inimplants can be useful during implantation to assist the surgeon inpositioning. The structures of the present invention may be rotatedlocally to increase the bulk density in certain locations to provide oneor more areas of radiopacity, increased radiodensity, radiolucency,increased radiolucency, lucency or increased lucency. As used herein, inreference to markers, increased radiodensity indicates that an area hasa higher radiodensity than the immediately surrounding area. Theexemplary embodiments disclosed herein may also include radiopaque orincreased radiodensity variable markers constructed using varioustechniques, including but not limited to, filling in certain cells,providing thicker struts on certain cells, or providing thicker orreinforced nodes where certain struts meet. In some embodiments, thevariable markers are a configured as a particular shape, such as acircle, rectangle, cross or “X” mark to assist in the location oralignment of the implant. In some embodiments, variable markers in theshape of one or more characters (letters, numerals, etc.), a name or alogo may be included in the implant. When a variable marker includescharacters, a name or a logo oriented to face in the desired direction,they can be visible on an x-ray as a lighter region. In the alternative,a void, area of lower density, or area of lower bulk thickness may beprovided to create a darker area on an x-ray representing a character, aname or a logo. When including a variable marker in the shape of one ormore characters, they can be added through the addition of a block ofmaterial or a void of material in the open cell structure in the shapeof the desired character(s). In some embodiments, the variable markersmay represent a barcode, QR (matrix) barcode, or other data encodingmethod such as filling of specific cells within the lattice as a methodof device serialization.

The variable markers disclosed herein can be used with theaforementioned lattice structures with high x-ray lucency to improve thevisibility of the variable markers in metallic materials. The variablemarkers can also be used in a lattice structure with a rotation gradientangled towards an x-ray focal point to provide a larger area on animplant with high x-ray lucency.

In some embodiments, the variable markers may be configured so that thevariable markers become more lucent during misalignment and more opaquewhen properly aligned (or vice versa). It would be useful to providevariable markers that increase or decrease in lucency when rotated toprovide a surgeon a clear indication of when an implant is aligned ormisaligned. In some embodiments, the variable markers may comprise abiocompatible lattice where the variable markers comprise orientationfeatures relative to other variable markers.

FIGS. 23-24 illustrate a first exemplary embodiment of the variablemarkers that uses selectively filled unit cells. Variable radiodensityas used in reference to the variable markers means that the markers haveat least a first radiodensity when viewed from a first direction and asecond radiodensity when viewed from a second direction. The variablemarkers may optionally have additional radiodensities when viewed fromadditional directions.

FIG. 23 illustrates an isometric view of the first exemplary embodimentof the variable markers shown in a lattice 110. The lattice 110 uses arepeating square unit cell, however other types of unit cells, as notedearlier, can be substituted. Within the lattice 110, two solid unitcells 121 & 122 have been added. The solid unit cells 121 & 122 can besolidly filled so that there are no voids within the planes that definethe cell walls, having a volumetric density of about 100%. They mayoptionally contain a central void, be filled with a material with avolumetric density of less than 100%, only partially filled or filledwith a material with a volumetric density of between and including 0% to30%. In the isometric view of FIG. 23, the solid unit cells 121 & 122are at a misalignment viewing direction, meaning that the solid unitcells 121 & 122 will show up as more radiolucent than in an alignedviewing direction.

FIG. 24 depicts a side view of the first exemplary embodiment of thevariable markers. The side view of the lattice 110 is shown from asecond misalignment direction where the location of the solid unit cells121 & 122 do not overlay one another in this view. As a misalignmentviewing direction, the solid unit cells 121 & 122 will show up as moreradiolucent than in an aligned viewing direction. In the first exemplaryembodiment, the aligned direction is 90 degrees in either directionabout a vertical axis from the side view in FIG. 24. If the lattice 110is rotated by 90 degrees in either direction about a vertical axis fromthe side view in FIG. 24, the solid unit cells 121 & 122 will overlayone another. With the volume of solid unit cells 121 & 122 overlapping,the area of the overlapped area will appear much more radiopaque than ina misalignment direction. Overlay, as used herein, refers to when amarker is at least partially in the same location relative to a viewingdirection. For instance, in an aligned direction, a marker closer to theviewer in a viewing direction could overlay a marker further from theviewer, creating a localized area with higher or lower lucency. If themarkers have a higher volumetric density that the surrounding structure,any marker overlay over another will create a localized are of lowerlucency. If the markers have a lower volumetric density that thesurrounding structure, any marker overlay over another will create alocalized area of higher lucency. An aligned direction can becharacterized by one marker only partially overlaying another marker. Amisaligned direction could be characterized by one marker partiallyoverlaying another marker, but not completely overlaying the othermarker.

FIGS. 25-27 illustrates a second exemplary embodiment of the variablemarkers that employs partially filled unit cells. FIG. 25 illustrates anisometric view of the second exemplary embodiment of the variablemarkers shown in a lattice 25210. The lattice 25210 used is a repeatingsquare unit cell, however other types of unit cells, as noted earlier,can be substituted. Within the lattice 25210, two partially filled unitcells 25231 & 25232 have been added. The partially filled unit cells25231 & 25232 can be solidly filled so that there is are no voids withinthe filled area. The filled area may optionally contain one or morevoids, be filled with a material with a volumetric density of less than100% or only partially filled. In the isometric view of FIG. 25, thepartially filled unit cells 25231 & 25232 are at a misalignment viewingdirection, meaning that the partially filled unit cells 25231 & 25232will show up as more radiolucent than in an aligned viewing direction.

FIG. 26 is a side view of the second exemplary embodiment of thevariable markers. The side view of the lattice 25210 is shown from analigned direction where the location of partially filled unit cells25231 & 25232 overlap in this view. The partially filled unit cell 25232is located behind partially filled unit cell 25231 in this view so thatwhen viewing the variable markers in the aligned direction, the x-raywould need to travel through both partially filled unit cells 25231 &25231, decreasing their radiolucency.

FIG. 27 illustrates an alternative side view of the second exemplaryembodiment of the variable markers. The alternative side view of thelattice 25210 is shown from a second alignment direction that can beused to highlight or identify a second direction to a user. Thepartially filled unit cells 25231 & 25232, in this example, arecomprised of a filled unit cell wall, with substantially square faces inthe aligned direction and narrow edges in the second alignmentdirection. The filled unit cell walls have a greater radiodensity fromthe narrow edge (their planar direction) than from the substantiallysquare faces because of the increased amount of bulk thickness in theplanar direction. The filled unit cell walls also have an elongatedshape when viewed in the planar direction rather than a substantiallysquare shape when viewed in a direction normal to the planar direction.Therefore, when viewing a single filled wall from a narrow edge orplanar direction, it will be elongated and be less radiolucent than thesame filled wall viewed from the direction of the square faces. Thedifference in radiodensity and appearance when viewed in the aligneddirection or second aligned direction can be amplified by addingadditional overlapping filled unit cell walls to increase the bulkthickness of the material in the aligned or second aligned directions.

FIGS. 28-31 illustrate a third exemplary embodiment of the variablemarkers that uses selectively enlarged nodes. FIG. 28 illustrates anisometric view of the third exemplary embodiment of the variable markersshown in a lattice 28310. The lattice 28310 comprises a repeating squareunit cell, however other types of unit cells, as noted earlier, can besubstituted. Within the lattice 28310, three enlarged nodes 28341-28343have been added. The enlarged nodes 28341-28343 can be solidly filled sothat there is are no voids within the filled area and a volumetricdensity of about 100%. The filled area may optionally contain one ormore voids, be filled with a material with a volumetric density of lessthan 100%, only partially filled, or filled with a material with avolumetric density of between and including 0% to 30%. In the isometricview of FIG. 28, the enlarged nodes 28341-28343 are at a misalignmentviewing direction, meaning that the enlarged nodes 28341-28343 will showup as more radiolucent than in an aligned viewing direction.

FIG. 29 depicts an offset side view of a third exemplary embodiment ofthe variable markers. In FIG. 29, the offset side view is a misalignmentdirection that is approaching a side aligned direction. In the thirdexemplary embodiment, the aligned direction occurs when the lattice28310 is rotated so that one or more enlarged nodes 28341-28344 areoverlapping. In FIG. 29, the enlarged nodes, 28341, 28342 & 28344partially overlay one another, but do not fully overlay one another.

FIG. 30 depicts a top view of the third exemplary embodiment of thevariable markers. The top view can be an alternative aligned directionif further enlarged nodes are located directly below enlarged nodes28341 & 28342. If no additional enlarged nodes are located belowenlarged nodes 28341 & 28342, the top view would be an additionalmisalignment view.

FIG. 31 depicts a side view of the third exemplary embodiment of thevariable markers. The side view of the lattice 28310 is shown from analigned direction where the location of enlarged nodes 28341 & 28342overlap in this view. Enlarged node 28342 is located behind enlargednode 28341 in this view so that when viewing the variable markers in thealigned direction, the x-ray would need to travel through both enlargednodes 28341 & 28342, decreasing their radiolucency.

FIG. 32 depicts a fourth exemplary embodiment of the variable markersthat uses selectively enlarged nodes. FIG. 32 depicts an isometric viewof the fourth exemplary embodiment of the variable markers shown in alattice 32410. The lattice 32410 used is comprised of a repeating squareunit cell, however other types of unit cells, as noted earlier, can besubstituted. Within the lattice 32410, two enlarged nodes 32441 & 32442have been added. The enlarged nodes 32441 & 32442 can be solidly filledso that there is are no voids within the filled area, having avolumetric density of about 100%. The filled area may optionally containone or more voids, be filled with a material with a volumetric densityof less than 100%, only partially filled or filled with a material witha volumetric density of between and including 0% to 30%. In theisometric view of FIG. 32, the enlarged nodes 32441 & 32442 are at amisalignment viewing direction, meaning that the enlarged nodes 32441 &32442 will show up as more radiolucent than in an aligned viewingdirection.

For the fourth exemplary embodiment, the aligned directions would fallin a lateral direction. One aligned direction could be viewed byrotating the lattice 410 from the orientation in FIG. 32 by about 45degrees about the x axis and about 45 degrees about the z axis. A secondaligned direction could be viewed by rotating the lattice 32410 from theorientation in FIG. 32 by about 45 degrees about the x axis and about135 degrees about the z axis.

FIGS. 33-34 illustrate a fifth exemplary embodiment of the variablemarkers that uses selectively enlarged struts. FIG. 33 illustrates anisometric view of the fifth exemplary embodiment of the variable markersshown in a lattice 33510. The lattice 33510 used is comprised of arepeating square unit cell, however other types of unit cells, as notedearlier, can be substituted. Within the lattice 33510, two enlargedstruts 33551 & 33552 have been added. The enlarged struts 33551 & 33552can be solidly filled so that there is are no voids within the filledarea, having a volumetric density of about 100%. The enlarged struts mayalso be employed using other characteristics, including but not limitedto, partially enlarged struts, enlarged struts between adjacent nodes,enlarged struts on an area centered over a node, struts smoothlyintegrated into the surrounding structure and/or struts sharplyintegrated into the surrounding structure. The filled area mayoptionally contain one or more voids, be filled with a material with avolumetric density of less than 100%, only partially filled or filledwith a material with a volumetric density of between and including 0% to30%. In the isometric view of FIG. 33, the enlarged struts 33551 & 33552are at a misalignment viewing direction, meaning that the enlargedstruts 33551 & 33552 will show up as more radiolucent than in an alignedviewing direction.

FIG. 34 is a side view of the fifth exemplary embodiment, showing thelattice 33510 in an aligned direction. In the aligned direction, theenlarged strut 33551 fully overlays the enlarged strut 33552 so thatonly enlarged strut 33551 is visible. The opposite side would also be analigned direction in this embodiment.

The variable markers disclosed herein can be implemented in varioustypes of implants, including the high x-ray lucency lattice structuresdisclosed herein, other porous structures and substantially solidstructures. The variable markers could be used in some solid metallicstructures and in some solid polymer structures, particularly PEEKstructures.

The variable markers can be designed relative to the lucency of the bulkvolume they are connected to, fixed to or contained within. The relativelucency of the bulk volume is best determined as an average baselinelucency representing the average lucency of the bulk volume in a givendirection without the inclusion or any variable markers. The averagebaseline lucency can be taken across the entire side of a bulk volume ifusing an infinite focal length, or across a focal area when using afinite focal length. Once the variable markers are included with thebulk volume, a second average lucency may be taken of the bulk volumeand the variable marker. It is preferable for the inclusion of avariable marker to change the average lucency of the bulk volume by 35%or less than the average baseline lucency when viewed in a misaligneddirection. It is more preferable for the inclusion of a variable markerto change the average lucency of the bulk volume by 15% or less than theaverage baseline lucency when viewed in a misaligned direction. In someembodiments, it is preferable for the inclusion of a variable marker tochange the average lucency of the bulk volume by an amount between andincluding 4% and 12% compared to the average baseline lucency whenviewed in a misaligned direction.

The variable markers can cause a change from the average baselinelucency that can be quantified in an aligned direction. When thevariable markers are in an aligned direction, they can cause a localizedchange in lucency compared to the average baseline lucency. It ispreferably for the variable markers to cause a localized change inlucency of at least 1% compared to the average baseline lucency. In someembodiments, it is preferable for the variable markers to cause alocalized change in lucency of at least 4% compared to the averagebaseline lucency. In some embodiments, it is preferable for the variablemarkers to cause a localized change in lucency of at least 15% comparedto the average baseline lucency. The localized change in lucency refersto a measure of lucency taken at an area local to the variable markerand used in comparison with the average baseline lucency. The area localto the variable marker can be measured as the visible area of a variablemarker when viewed in an aligned direction. In some embodiments, thearea local to the variable marker can be measured as an area including avariable marker when viewed in an aligned direction and including anarea near the variable marker of about one to ten times the visible areaof the variable marker when viewed in an aligned direction.

The variable markers disclosed herein can comprise a marker with variousvolumetric density properties. In some embodiments, the variable markershave a volumetric density of about 100%. In some embodiments, thevariable markers have a volumetric density of less than 100%. In someembodiments, the variable markers have a volumetric density of betweenand including 0% to 30%. In some embodiments, the variable markers havea volumetric density of between and including 0% to 25%.

FIGS. 35-36 illustrates an example of an implant 35660 that includesdiagonal variable markers 35661 & 35662. FIG. 35 is a side view of theimplant 35660 in an aligned direction. In the aligned direction, thediagonal variable marker 35661 fully overlays the diagonal variablemarker 35662 so that the area is less radiolucent than the surroundingbody of the implant. The diagonal variable markers 35661 & 35662 in theexemplary embodiment comprise struts with a diameter of approximatelyone mm and configured to overlap at the aligned direction. In the sideview of FIG. 35, the aligned direction, the diagonal variable marker35661 is largely radiopaque due to a significant overlap with thediagonal variable marker 35662. When the diagonal variable markers 35661& 35662 are viewed in the aligned direction, the closer marker to theviewer partially or fully overlays the more distant marker from theviewer. FIG. 36, where the implant 35660 is rotated approximately 45degrees about the z axis from its position in FIG. 35 to a misaligneddirection, the diagonal variable markers 35661 & 35662 become moreradiolucent than when viewed from the FIG. 35 orientation as the amountof overlap between the struts decreases.

The implant 35660 also includes another variable marker 35663 configuredfor providing a measure of alignment. In the aligned view of FIG. 35,the variable marker 35663 is fully radiolucent. The variable marker35663 is provided as an elongate lateral opening in the implant,however, other structures are possible. In some embodiments, thevariable marker 35663 can be multiple discrete openings or voids thatappear in a line away from the viewer in the aligned view and appearindividually in a misaligned view. In some embodiments, the variablemarker 663 can be multiple omitted struts, omitted nodes, smaller strutsthan the surrounding structure or smaller nodes than the surroundingstructure that appear in a line away from the viewer in the aligned viewand appear individually in a misaligned view. In the misaligned view ofFIG. 36, the variable implant marker 35663 is hidden by the moreradiodense surrounding structure.

FIGS. 37-38 depict an example of an interbody fusion implant, designedusing the high x-ray lucency lattice and methods of designing a highx-ray lucency lattice disclosed herein, and imaged on an x-ray machine.The image in FIG. 37 was taken from the anterior to posterior directionand the image in FIG. 38 was taken in a lateral direction. These x-rayimages of a first implant 760, a second implant 860 and a third implant960 were taken from predetermined desired directions, which are theanterior to posterior and lateral directions in this case. The exemplaryimplants 760, 860 & 960 include endplates with a higher volumetricdensity than the lattice body, making the endplates appear darker in thex-ray image than the lattice body. The fixation rods and screws oneither side of the implants 760, 860 & 960 were not constructed ordesigned according to the disclosure herein and are largely radiopaque.In comparison, the lattice body portion of the implants 760, 860 & 960constructed and designed according to the disclosure herein aresignificantly more radiolucent than the fixation rods and screws.

What has been described is a biocompatible lattice with high x-raylucency, a method of designing a lattice with high x-ray lucency,variable markers for use in medical implants with at least a degree ofradiolucency, a method of designing variable markers for use in medicalimplants with at least a degree of radiolucency and a method of usingvariable markers in medical implants with a degree of radiolucency. Inthis disclosure, there are shown and described only exemplaryembodiments of the invention, but, as aforementioned, it is to beunderstood that the invention is capable of use in various othercombinations and environments and is capable of changes or modificationswithin the scope of the inventive concept as expressed herein.

The invention claimed is:
 1. A method for designing a porous structurehaving an increased lucency property, the method comprising: generatinga bulk volume comprising a plurality of repeating structures in a formcapable of analysis by an analysis tool, wherein the analysis tool isconfigured to analyze at least one of a strut diameter, a cell height, acell width, a cell depth, a device thickness, a device height, and adevice length in order to determine at least one rotation angle of thebulk volume; propagating the bulk volume at an orientation determined atleast in part by the at least one rotation angle of the bulk volume;calculating a uniformity of bulk thickness across the structure along adesired direction for viewing, wherein the desired direction correspondsto a direction along which the increased lucency property is desired;iterating across rotations of the bulk volume to identify a desiredmaximum uniformity of bulk thickness; capturing the at least onerotation angle of the bulk volume at which the desired maximumuniformity of bulk thickness occurs; generating a final structure forthe porous structure based on the captured at least one rotation angle;and displaying at least a portion of the final structure forvisualization via a visualization tool.
 2. The method of claim 1,wherein the visualization tool comprises a 2D heat map of the structurein the desired direction.
 3. The method of claim 1, further comprisingcalculating the uniformity of the bulk thickness using a coefficient ofdetermination.
 4. The method of claim 1, wherein the plurality ofrepeating structures comprise a lattice structure.
 5. The method ofclaim 4, wherein the lattice structure comprises at least one of aradial dodeca-rhombus geometry, a rhombic dodecahedron geometry, amodified rhombic dodecahedron geometry, a diamond geometry, adodecahedron geometry, a square geometry, a pentagonal geometry, ahexagonal geometry, an octagonal geometry, a sctet struts geometry, atrunic octa geometry, a diagonal struts and rounded geometry, areinforced geometry, and a weakened geometry.
 6. The method of claim 4,further comprising selecting a focal length for the porous structure. 7.The method of claim 1, further comprising sectioning the bulk volume toone or more segments corresponding to approximate dimensions of aselected implant type.
 8. The method of claim 1, further comprisingdetermining the desired maximum uniformity of bulk thickness based on atleast one of relative dispersion and relative disparity of the porousstructure.
 9. The method of claim 1, further comprising translating theporous structure from its original orientation to a second orientation.10. A method for designing a porous structure having an increasedlucency property, the method comprising: generating a bulk volumecomprising a plurality of repeating structures in a form capable ofanalysis by an analysis tool, wherein the bulk volume is sectioned intoone or more portions corresponding to approximate dimensions of animplant type, wherein the analysis tool is configured to analyze atleast one of a strut diameter, a cell height, a cell width, a celldepth, a device thickness, a device height, and a device length in orderto determine at least one rotation angle of the bulk volume; propagatingthe bulk volume at an orientation determined at least in part by the atleast one rotation angle of the bulk volume; calculating a firstuniformity of bulk thickness across the structure along a first desireddirection for viewing, wherein the desired direction corresponds to adirection along which the increased lucency property is desired;calculating a second uniformity of bulk thickness across the structurealong a second desired direction for viewing, wherein the second desireddirection for viewing corresponds to a direction along which a secondlucency property is desired; iterating across rotations of the bulkvolume to identify a desired first uniformity of bulk thickness alongthe first desired direction for viewing and a desired second uniformityof bulk thickness along the second desired direction for viewing; andcapturing at least one rotation angle of the bulk volume at which thedesired first uniformity of bulk thickness occurs along the firstdirection and at which the desired second uniformity of bulk thicknessoccurs along the second direction; generating a final structure for theporous structure based on the captured at least one rotation angle; anddisplaying at least a portion of the final structure for visualizationvia a visualization tool.
 11. The method of claim 10, further comprisingdetermining the desired uniformity of bulk medium along at least one ofthe first and second directions based on at least one of relativedispersion and relative disparity of the porous structure.